How I Teach Factoring Quadratics

29 January 2017

How I Teach Factoring Quadratics

I know of a few different methods people use to teach factoring, but I’ve never been a fan of the “fancy” methods.  They just don’t work for me.  When I teach factoring, I actually teach the unit backwards.  I teach factoring by grouping, factoring trinomials when a≠1, factoring trinomials when a=1, then special cases.

I start with factoring by grouping, because once students can do that, factoring trinomials is easy.  I tend to spend an extra day teaching factoring by grouping.  When students have that down, I move on to factoring trinomials.  I prefer teaching when a≠1 first, because when a=1 is really just a special case.  If students can handle the “harder” version, there almost isn’t a need to teach the “easier” version.

So, this is how I teach factoring.  This is not revolutionary.  It is not new, or even interesting.  But it works, every time.  I've often heard this method called "splitting the middle".

First, I have students multiply the “a” value by the “c” value.

How I Teach Factoring Quadratics
Then, I tell them they are looking for two numbers that multiply to that value.  I have them make a list.

How I Teach Factoring Quadratics

Only after that do I have them find the pair of numbers that adds to the “b” value.

How I Teach Factoring Quadratics

Next, I have students split the middle and finish by factoring by grouping.  So, example student work for the example would look like this:

How I Teach Factoring Quadratics

I prefer to teach factoring this way because it doesn’t rely on tricks and it works every time.  Also, after this lesson, teaching a=1 is just a special case.

6 comments:

  1. I use the same method when teaching factoring, although I LOVE that you teach the a=1 case after because I always have a student or two who get confused between the two strategies. I think that would help a lot. Thanks!

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  2. I do this in a similar manner, but when I have them do the factor by grouping I have them put it into an area model. The graphic organizer helps them to see where the common factors are. It works for solving quadratics where a is not 1 as well as cubic expressions that can be factored by grouping. It's also a method I teach to multiply polynomials for those who need their work to be more organized than just distributing.

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  3. Great strategy. I enjoy the hands on method of teaching quadratics using Mortenson math blocks. I had some of my own personal "ah, ha" moments playing around with quadratics.

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  4. I teach special education students and use this same method, in the same order. Your'e right. It works every time. I find I rarely have to teach a=1 because they don't see it as any different. When you multiply a*c, it doesn't matter if a=7 or a=1.

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  5. I've been doing this for a few years - it also makes it easier when you have to go into factoring four or more terms because they already know how to factor by grouping

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  6. Over (too many) years of teaching, I have seen and used numerous techniques to factor quadratics (from guess-and-check to box-method) .... this is my favorite and the most easily understood.

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